A piece of hot metal is cooling at a linear rate. Its Temp. After 4 minutes is 310 deg. Its Temp. After 7 minutes is 205 deg. When will the object be 30 deg.?

It'll take 12 minutes to be at 30 degrees.

Step-by-step explanation:

Since the metal is cooling at a linear rate then the rate of degrees per minute should be the through the cooling process. From 4 minutes to 7 minutes there was a span of 3 minutes and in that time the metal cooled 105 degrees. So the metal is cooling at a rate of

rate = 105/3 degrees/minute = 35 degrees/min

To reach 30 degrees from 205 it should cool down an additional 175 degrees so it'll take:

minutes = deegrees/rate = 175 / (35) = 5 minutes

Since the metal had a temperature of 205 degrees in 7 minutes, then it'll take 12 minutes to be at 30 degrees.